By Daniel Mahoney
Commodity markets current a number of demanding situations for quantitative modeling. those comprise excessive volatilities, small pattern information units, and actual, operational complexity. furthermore, the set of traded items in commodity markets is extra constrained than in monetary or fairness markets, making price extraction via buying and selling more challenging. those evidence make it really easy for modeling efforts to run into critical difficulties, as many types are very delicate to noise and therefore can simply fail in perform.
Modeling and Valuation of strength buildings is a finished advisor to quantitative and statistical methods which have been effectively hired in aid of buying and selling operations, reflecting the author's 17 years of expertise as a front-office 'quant'. the main subject of the publication is that easier is mostly greater, a message that's drawn out throughout the fact of incomplete markets, small samples, and informational constraints. the required mathematical instruments for realizing those matters are completely constructed, with many recommendations (analytical, econometric, and numerical) gathered in one quantity for the 1st time. a selected emphasis is put on the imperative position that the underlying industry solution performs in valuation. Examples are supplied to demonstrate that strong, approximate valuations are to be hottest to overly formidable makes an attempt at targeted qualitative modeling.
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Example text
The incremental contribution of information dies off as the time horizon in question grows (asymptotically flattening variance scaling law). The effect of jumps/outages is similar to heat rate/demand, but on the supply side. Knowing that a unit has gone done when we are far from maturity will not affect our expectations nearly as much as when the unit goes down near expiry. 43). Whatever the intensity of jumps is, far from the maturity the exponential term is close to 1. Of course, the rate at which capacity is restored to the stack (effectively, the mean-reversion rate κl ) determines the horizon over which we can say this or that piece of information is unimportant (for forming expectations).
17) becomes a non-stationary process. 21) become trivial! What is going on of course is that the estimator is converging at a rate faster than O( √1 ), in fact with rate O( T1 ). 22) where w is a standard Brownian motion. 22) has a nonstandard distribution and the critical values (for acceptance/rejection of inferences) are typically obtained via simulation. The point we are trying to make here is that, in the presence of non-stationary, the relevant diagnostics can radically change, even if the underlying estimation algorithm is unchanged.
This seemingly minor change actually has major ramifications for the underlying scaling law. 46) is that as time-to-maturity tends zero, so does this modulation factor. Moving away from expiry, this factor initially grows, until eventually dying out. , κθ = 0), the factor actually asymptotes to 1. The thrust of this behavior is that, close to maturity, jumps in the mean-reversion level have little effect on expectations of future heat rate. However, sufficiently far from maturity, these jumps do have a definite effect on expectations.